sram cx1 without the sram cx1 crankset?
Strangely enough, everything seems to say that 11 speed plays nicely together - chain widths, etc. 

The crankset area (since you're running a 1x11) is effectively independent of the stuff going on in the rear (where the CX-1 groupset has a rear derailleur, shifter, cassette, etc.). So, you shouldn't have to change to a SRAM CX-1 crankset (unless you wanted to make everything match for some reason).