M&N

Algebra Level 3

Given that:

\({ \left( \sqrt { 125 } +\frac { \sqrt { 5 } +4 }{ 2\sqrt { 5 } -3 } \right) }^{ 0.5 }\times \sqrt { 3\sqrt { 5 } -1 } =\quad m\sqrt { n } \)

Where m and n are integers, find the value of \(m+n\).

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