If \(xy=6\) and \(x^2 y + y^2 x + x+ y=63 \). Let \(S\) denote the sum of digits of the number \( (x^4+y^4)(x^3+y^3)(x^2+y^2)(x+y) \).

Find the value of \( \sqrt[3]{\sqrt S + \frac S4 + \frac S3 } \).

\(Note\):You can use calculator at final calculation.

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