How to test balance between right and left channel

If your system has the ability to adjust the balance level, I would just do that and enjoy the music, after all, that is what the balance control is there for.

if it has vu meters, than you can play mono record on stereo pick-up.

If your system has the ability to adjust the balance level, I would just do that and enjoy the music, after all, that is what the balance control is there for.

And if no balance control, I have had success in different rooms by just moving one speaker in or out, in both cases by only an inch or two.

But if you want to make sure your equipment is functioning properly than I can understand.
If testing with equipment isn't practical, I would play a mono recording and listen to where the image is centered. Then I would swap cables down the chain to see if the image stayed in the same spot or moved left or right.

You can also play some white noise and use an spl meter. Sometimes if your room is an odd shape or doesn't have consistent lighting, it can be hard to judge. Kind of like an optical illusion.

A Stereophile Test CD has L & R mono tracks if I'm remembering correctly. You will need a sound pressure level (SPL) meter and you should be set. There are also many other tests that are helpful.