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


Back in my day the only time we started panic buying was when the bartender shouted "last call"!

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