If you want to use the cube root approach, it should be done on a state-by-state level, not a total US population. This would effectively prevent larger states from dominating smaller states.
So a state with 1,000,000 people would get 100 representatives, whereas a state with 27,000,000 would get 300 reps.
Otherwise, leave it as is, asany increase in reps would tilt the balance to large states, which would be the end of the republic.
I don’t think it would tilt the balance any more than the current apportionment. But it would dilute the power of Congress, and be consistent with Article 1, Section 2.
I think that’s what the Senate is for, and why there are two houses of Congress.
The Senate, with two Senators no matter how small or large the state, is supposed to address that very problem.