I did a search for the minor 6 chord and I found that this refers to the minor triad with an added major 6th interval (or 13th rather). I am studying a song that has a minor triad with a minor 13th interval. What do you call this chord?
It's quite happy being a m6, with the major 6th note just above the P5 - as in A C E F#. It doesn't have to be 13, in fact it usually isn't. Flatten the major 6 to an Fn, and the notes are A C E F. It's not an A minor derivative now, but an Fmaj7. With the A as its lowest note, it's known as Fmaj7/A. The first inversion of Fmaj7.