Wouldn't it overdrive? I can't understand why anyone would need to do that...No line out?
A DI would be the best bet, skip to the bottom if you want to do it right.....but.., if you absolutely need a signal to the mixer, RIGHT NOW, with just whats laying around, I think you can get an unbalanced line out by running a cable from the second input on your amp to the mixer, I know you can get a signal that way from an old Fender bassman, I vaguely remember seeing someone do it when I was a kid{that was 30 years ago however}
Another zero budget way (at least better than running the hot line to the mixer) would be to cut 2 instrument cables in half, then twist or solder them together to make a Y adapter. then plug one end into the MIC input on the mixer(the MIC setting will boost it a bit). That is going to sound weak and lifeless compared to a proper balanced signal, but you will safely get a signal.
IF the reason you want to go from your speaker output to the mixer because you need a hotter signal than plugging direct, you could use a Headphone, or Turntable preamp, those might be noisy, ok for practice or even live maybe, will totally suck for recording.
The best solution (which you probably figured out) would be to use a proper DI box, I like the Radial for recording, I have a bunch of them, they always seem to work and do nothing at all to color the sound *(to my ears). IF you DO want to color the sound, and can't afford a REDDI, the ART studio tube preamp has a 12ax7 valve, and if you put a nice tube in it (actually I'm not sure what the stock tube is like, I always swap em first thing -probably fine.) they warm up the sound nicely for live sound, they don't seem to last very long, I get about a year before they start getting crackly.
ALSO you need to use a DI in case you experience Phase cancellation, a lot of times when your mix sounds weak or funny, you just have something out of phase, flipping the phase switch can fix that. No DI, No phase switch.
Balanced VS Unbalanced--
Unbalanced connection is a grounded connection that can can have background noise, interference and loss of clarity, especially if it's a long cable, or is going thru a bunch of connections, A balanced line is a 3 way connection, ground, live AND return what happens with this is that noise is cancelled out because of a couple reasons (I don't understand them all, sound is magic) part it is done by the amplifier, noise on both signals cancels each other out at the amp ,part is accomplished just by having the two wires so close to each other ; xlr cables are twisted inside--that prevents induction (interference),and the shield is just a shield not the ground so no cross talk or any funny business....probably some other things I haven't learned yet.
I hope that helps, I know a lot of times I wonder things like that "what if I connect the speaker out to the mixer???"[well, not that], and you get plenty of answers like "NO!", a few people take the time to explain why it's a bad idea, but half the time the reasons are over my head, a little research into the answers usually clears it up tho.
SO...What happened when you ignored everybody and did it anyway? I'm guessing it worked, but sounded like a tube screamer on low.