Technically a C11 is as you indicated,C-E-G-Bb-D-F. Many eliminate the E to avoid dissonance, however that is an option and not a rule. Thus playing it either way is legal.

PS - it really depends on your ear and the melody. Sometimes having the E sounds good and sometimes it doesn't. YMMV


I'm no longer allowed to go caroling at the psych hospital.
I guess Do You Hear What I Hear was a bad song choice!

64 bit Win 10 Pro, the latest BiaB/RB, Roland Octa-Capture audio interface, a ton of software/hardware