A rad problem

Algebra Level 4

\[ \large \sqrt{\frac{16+\sqrt{31}}5 } + \sqrt{13 - 12\sqrt{1 - \left( \frac{9-\sqrt{31}}{20} \right)^2 } } \]

If the above expression can be represented in the form \( \sqrt{x} \), then find \(x\), where \(x\) is square free.

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