Negligible radicals

Algebra Level 3

$\large {\frac { { (4+\sqrt { 15 } ) }^{ \frac { 3 }{ 2 } }+{ (4-\sqrt { 15 } ) }^{ \frac { 3 }{ 2 } } }{ { (6+\sqrt { 35 } ) }^{ \frac { 3 }{ 2 } }-{ (6-\sqrt { 35 } ) }^{ \frac { 3 }{ 2 } } } }$

If the value of the expression above equals to $\frac a b$ for coprime positive integers $a,b$. What is the value of $a+b$?

This problem is a part of the set 1+2=3
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