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 $$a+b$$?

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