@GTs58 knows the serials better than I do, but I can tell you just about everything on that bike has been swapped out. The CM would be clubman... I will look more into the X serial.
Those decals...someone sliced and diced two different model sets together: the down tube and the seat tube decals are the same and supposed to be off the seat tube location of a 1960 continental; the chain guard decal is supposed to be on the down tube of a 1960 continental; the decal at the head badge is supposed to be the seat tube decal of an early 60s schwinn traveler; the top tube decal is supposed to be the down tube location of an early 1960s traveler.
The chain guard looks like it is off an early 60s black traveler (the chrome top and black side is that setup on those). Saddle is swapped off another schwinn. Pedals are some random rat traps, looks 60s. The front fender is a peaked fender which is found on various Schwinn lightweights at different times but this one doesn't look correct and might be off another brand bike. The peak doesn't match the Schwinn type. That rear fender, no idea. I can't remember off the top of my head where I have seen the brace attachment to fender like that (edit: I didn’t see at first that someone welded the braces together). There is a tab welded on to the seat stay and someone did that after the fact. Which also shows the bike was repainted at some point. The head badge location shows the horizontal badge screw alignment which would be superior, continental or new world (in this era). The crank setup looks like a mid to late 1940s continental. The rear wheel definitely looks like a replacement off something because this frame appears older than 1956. See if you see any stampings/markings on the rims (front/back). Front wheel hub is hard to see but doesn't look Schwinn. The stem looks like the
taller version of the double adjustable stem which also came on the 40s continental, but not this tall version (could be wrong on this but I thought they were shorter). Brake levers look early 50s Schwinn lightweight (52/53). Bars look like 40s/50s continental, new world or traveler. Brake calipers look like they are the early 50s type that are on travelers, but hard to know. See if you see any markings. All brake lines are newer so I am sure someone messed with that stuff too. Can barely see the shifter but looks like a Sturmey 70s plastic replacement. Seat clamp is hard to see. Edit:
I keep looking at that headset...looks funky. I can’t place it. Nevermind it’s likely original. Oh and the grips are original...
Someone had fun on this one! To me it looks like it started out a 40s Schwinn Continental Clubman and was probably stripped of parts at some point and then someone tried to put it back together with what they could. Usually the crank setup is left intact because no one knows how to get the cotter pins out haha.