Yup. Those are tough.

Chordelius is one of my my worst games in general, but I had particular trouble with the levels that focused on the difference between those two. Eventually made it through that, but now I'm on the levels with 6/7, 6/9, and 7/9 chords. Joy.

The fun part for me is that I don't have a problem with them in chordelius, but have issues with them in calibrator.

No, you are not alone! In some sense, at least for me, the M6 appears to be more Major flavor and the m6 more minor (although it's the other way round looking from the octave above).
It was helpful for me, to present an M6 and an m6 to my ears on my piano / synth (not in the same pitch) and I made progress by this.

I use private investigations for the m6 ref. It’s pretty distinctive

The 6th is the same note for a m6 or M6 chord. The M6 is 1-3-5-6 and m6 is 1-b3-5-6. With solfege it is Do-Mi-Sol-La and Do-Me-Sol-La.
So for a 6 chord, the six is always La (or the major 6th). It confuses a lot of people until finally realizing that point. Does that help?

How about trying song starters?

m6 could be The Entertainer -

M6 could be My Bonnie lies over the ocean -

So - are you talking about the INTERVALS m6 and M6 or chords vi and VI? Your post is a bit confusing.

Song starters work very well for recognizing intervals. For me M6 is always recognizable as Sinatra's My Way first notes (And now...), and m6, is easily recognizable as Прекрасное далёко chorus starter, which, judging from your name might be familiar to you

nice, thank you! that name is familiar to me, as I used to love that song 2 years ago, especially the movie version.