Segment Information - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended			9 Months Ended		12 Months Ended
	Sep. 29, 2019	Dec. 30, 2018	Sep. 30, 2018	Sep. 29, 2019	Sep. 30, 2018	Dec. 30, 2018
Revenue, Major Customer [Line Items]
Total revenues	$ 403,706	$ 395,834	$ 385,231	$ 1,201,734	$ 1,265,305	$ 1,661,139
Domestic Company-owned restaurants
Revenue, Major Customer [Line Items]
Total revenues	165,135		158,285	490,594	529,906
North America franchising
Revenue, Major Customer [Line Items]
Total revenues	15,924		12,806	53,215	61,524
North America commissary
Revenue, Major Customer [Line Items]
Total revenues	154,703		146,240	450,735	461,408
International.
Revenue, Major Customer [Line Items]
Total revenues	24,679		25,653	75,843	84,836
International. | International other revenue
Revenue, Major Customer [Line Items]
Total revenues	(5,209)		(5,210)	(17,156)	(16,354)
International. | International eliminations
Revenue, Major Customer [Line Items]
Total revenues			70	191	213
All others
Revenue, Major Customer [Line Items]
Total revenues	43,265		42,247	131,347	127,631
All others | International other revenue
Revenue, Major Customer [Line Items]
Total revenues	5,209		5,210	17,156	16,354
All others | International eliminations
Revenue, Major Customer [Line Items]
Total revenues			(70)	(191)	(213)
Operating segments
Revenue, Major Customer [Line Items]
Total revenues	403,706		385,231	1,201,734	1,265,305
Operating segments | Company-owned Restaurants
Revenue, Major Customer [Line Items]
Total revenues	165,135		158,285	490,594	536,143
Operating segments | Commissary Sales
Revenue, Major Customer [Line Items]
Total revenues	217,497		208,775	637,860	666,287
Operating segments | Franchise Fees
Revenue, Major Customer [Line Items]
Total revenues	26,020		22,411	84,121	91,132
Operating segments | Other Sales
Revenue, Major Customer [Line Items]
Total revenues	62,627		56,439	184,296	174,443
Operating segments | Domestic Company-owned restaurants
Revenue, Major Customer [Line Items]
Total revenues	165,135		158,285	490,594	529,906
Operating segments | Domestic Company-owned restaurants | Company-owned Restaurants
Revenue, Major Customer [Line Items]
Total revenues	165,135		158,285	490,594	529,906
Operating segments | North America franchising
Revenue, Major Customer [Line Items]
Total revenues	15,924		12,806	53,215	61,524
Operating segments | North America franchising | Franchise Fees
Revenue, Major Customer [Line Items]
Total revenues	16,536		13,270	55,287	64,023
Operating segments | North America commissary
Revenue, Major Customer [Line Items]
Total revenues	154,703		146,240	450,735	461,408
Operating segments | North America commissary | Commissary Sales
Revenue, Major Customer [Line Items]
Total revenues	202,302		192,263	590,851	614,797
Operating segments | International.
Revenue, Major Customer [Line Items]
Total revenues	29,888		30,793	92,808	100,977
Other revenue from marketing fund contributions and sublease rental income	5,200		5,100	17,000	16,100
Operating segments | International. | Company-owned Restaurants
Revenue, Major Customer [Line Items]
Total revenues					6,237
Operating segments | International. | Commissary Sales
Revenue, Major Customer [Line Items]
Total revenues	15,195		16,512	47,009	51,490
Operating segments | International. | Franchise Fees
Revenue, Major Customer [Line Items]
Total revenues	9,484		9,141	28,834	27,109
Operating segments | International. | Other Sales
Revenue, Major Customer [Line Items]
Total revenues	5,209		5,210	17,156	16,354
Operating segments | All others
Revenue, Major Customer [Line Items]
Total revenues	38,056		37,107	114,382	111,490
Operating segments | All others | Other Sales
Revenue, Major Customer [Line Items]
Total revenues	57,418		51,229	167,140	158,089
Elimination
Revenue, Major Customer [Line Items]
Total revenues	(67,573)		(60,679)	(195,137)	(202,700)
Elimination | North America franchising
Revenue, Major Customer [Line Items]
Total revenues	(612)		(464)	(2,072)	(2,499)
Elimination | North America commissary
Revenue, Major Customer [Line Items]
Total revenues	(47,599)		(46,023)	(140,116)	(153,389)
Elimination | International.
Revenue, Major Customer [Line Items]
Total revenues			(70)	(191)	(213)
Elimination | All others
Revenue, Major Customer [Line Items]
Total revenues	$ (19,362)		$ (14,122)	$ (52,758)	$ (46,599)