Simplify!

Algebra Level 4

The value of (4+15)32+(4−15)32(6+35)32−(6−35)32\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 ab\large \frac{a}{b}, where a\large a and b\large b are positive, coprime integers. Determine the value of a+b\large a+b.

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

Satvik Golechha by Satvik Golechha
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