\[ \begin{eqnarray} m&=&\sqrt[3]{\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}-1} \\ n&=&\sqrt[3]{\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}+2} \end{eqnarray}\]

Let the values of \(m\) and \(n\) be described above. Compute \(2(20m+6n)^{2}-32\).

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