Everyone should love algebra more than geometry

Geometry Level 5

A square having sides parallel to the coordinate axes is inscribed in the region \(\{(x,y): x,y > 0,\)\(y< -x^{3} + 3x\}\). If the area of the square is written as \(A^{1/3} + B^{1/3}\) where \(A, B\) are integers and \(A>B\), then what is the circum-radius of triangle \(OPQ\) where \(O\) is the origin, \(P(A^{1/3},0)\) and \(Q(0, B^{1/3})\)?

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