The finest surds ever!

Algebra Level 4

\[\dfrac{(4+\sqrt{15})^{3/2}+(4-\sqrt{15})^{3/2}}{(6+\sqrt{35})^{3/2}-(6-\sqrt{35})^{3/2}}.\]If the value of above surd is equal to \(\dfrac{a}{b}\),where \(\text{gcd}(a,b)=1\), find \(a+b.\)

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