Algebra Level 5

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

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

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