Consider the parabola \(y^2 = 4x \).

Let \(P\) and \(Q\) be two points \((4,-4)\) and \((9,6)\) on the parabola.

Let \(R\) be a moving point on the arc of the parabola between \(P\) and \(Q\).

Find the maximum possible area of \(RPQ\).

If maximum area is \(S\), report your answer as \((4S)^{1/3} \).

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