WP says:
The brightest-known M-class main-sequence star is M0V Lacaille 8760, with magnitude 6.7 (the limiting magnitude for typical naked-eye visibility under good conditions is typically quoted as 6.5), and it is extremely unlikely that any brighter examples will be found.
I think what this really tells us is that there is no perfectly well-defined answer to this question. Looking at planetmaker's linked search, Itit seems like as you go from main-sequence K0 to main-sequence M0, it gets more and more doubtful/fuzzy whether the human eye can see any star at this magnitude.
It sounds like it would be a super fun project -- but not an easy one -- to try to observe M0V Lacaille 8760. You'd probably want to recruit a young person, create a very detailed finder chart, and go to a remote dark-sky location at high elevation. You'd probably need to create some pretty elaborate protocol to make sure that the person really did see it. Maybe you'd need to do it as a blind or double-blind experiment, with controls where the person was told to look for a star where there was none.