In jazz the A on the bottom of a Cm chord would be desiginated Am7-5.
Some would probably think a Cm6 is easier to understand. Everyone hears something different. Am7-5 sounds more difficult. Kind of like I know more than you about chords.
I never could understand in chord theory why the simple number system isn't use instead of the alphabet. If you can count to 13 you can be taught chord building a lot easier for playing around the home for your own entertainment.
I wonder how many people didn't buy computers because of terminology. Like disk drive. That had to scare the heck out of a lot of people. Recorder they would have understood right off the bat. It does record stuff ,right.
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I'm not prejudiced, I hate everybody!! Ha ha! My Sister-In-Law had this tee shirt. She was a riot!!!