There's an older related post on this topic: How do I adjust audio balance of my Android phone headphones out? – but it seems that it's not matching recent versions of Android anymore. Like this CNET post it recommends going to Settings › Accessibility and check the "Hearing" section (which I could not found on my Lollipop devices – according to the linked question, it might be device-specific and not available on all devices – the Samsung S6 e.g. seems to have this, for other devices it seems to have been removed) for either the "Sound balance" or the "Music Effects" item. So if your device has that: great, you're done!
If your device does not have this setting, there are 3rd party solutions. But as far as I am aware, they all require your device being rooted. If that condition is met, you can e.g. use:
As much as I've looked around, these seem to be the only options available currently.
Update by Victor Spinei after evaluation:
In order to download and install this you might need to check:
- Settings/Security/Unknown source to be ON
- Settings/Google/Scan device for security threats to be OFF
- Close security applications like Lookout
- Do not forget to restart all those services after installing the audio apps.