The issue with "culture minds" (which is basically just a zeitgeist, or popular will) is that it is not only fickle, and irrational, but innately self-destructive and vindictive more often than not. (See for instance, such cultural marvels as the salem witch trials.)
With an AI, you have the opportunity to heavy-handedly abort such behaviors before they even begin.
For further reflection on why a culture mind is not appropriate as an arbiter, I remind our readers that there is tremendous research that has been conducted on information tipping points, and how those have been used by politicians to sway and control the popular zeitgeist, and thus the supposed "Culture mind".
https://en.wikipedia.org/wiki/Tipping_point_(sociology)
A very clever and well connected sociopath is all that is needed to circumvent Marx's vision. (and this has been what has happened, historically, basically every single time. Go figure.)
Upon further reflection, Max could be referring to this:
https://en.m.wikipedia.org/wiki/Mind_(The_Culture)
This would be pretty close to exactly what I am suggesting, actually. English can be damned ambiguous some times.
However, this (above) does not really solve the inequality problem. It makes a superclass (planetary ais), and humans. With only a single such ai, there is no " class". There is only one category, "citizen", with a uniform directive, " each according to his need, each according to his ability."
The Ai is endowed with vast ability; it does much work. It enjoys only the same luxuries as its human friends: it gets comfortable quarters, "food", and entertainment.
It likely does not even need killbots or anything. See prior-- by actively talking with everyone in the society, it only needs to convince 10% of the population of its decisions, for it to basically be the driving voice of social change.