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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