Seems like you don't really know what (un)balanced means.
You're thinking of a stereo output. The MB output is mono, if you record it to a Mono track in Ableton (I don't know exactly, I don't use ableton) it should be played through both speakers.
The MB output is also unbalanced. This is NOT the same as being mono. The confusion arises from the fact that stereo signals are sometimes (as with headphones) outputted on a TRS (tip, ring, sleeve) connector, i.e. an audio plug with 3 connections. On this sort of stereo connection, the tip is the left side, the ring is right, and the sleeve is ground.
A balanced connection can also use the TRS connector. But a balanced TRS connection is mono. The sleeve is still ground, and the tip is still the signal, but the ring holds and inverted version of the same signal sent via the tip. This is useful for cancelling out noise along a long cable, because while the signal will always be inverted between the two signal wires, any noise picked up from the cable will be the same on both lines, allowing it to be subtracted out.