Simplify!

Algebra Level 4

The value of \(\Large \frac{(4+\sqrt{15})^\frac{3}{2}+(4-\sqrt{15})^\frac{3}{2}}{(6+\sqrt{35})^\frac{3}{2}-(6-\sqrt{35})^\frac{3}{2}}\) can be expressed in the form \(\large \frac{a}{b}\), where \(\large a\) and \(\large b\) are positive, coprime integers. Determine the value of \(\large a+b\).

This problem was taken from Higher Algebra by Hall & Knight.

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