Equate it

Algebra Level 3

2(2+6)3(2+3)\large \frac{2 ( \sqrt{2} + \sqrt{6} ) }{3 ( \sqrt{ 2 + \sqrt{3} } ) }

If the expression above can be written as mn\frac mn where m and n are coprime positive integers, find m+n m + n .

This problem is a part of the sets - 3's & 4's & " N " for number theory.
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