An algebra problem by Mateo Matijasevick

Algebra Level 3

\[\dfrac { { \left( 4+\sqrt { 15 } \right) }^{ \frac { 3 }{ 2 } }+{ \left( 4-\sqrt { 15 } \right) }^{ \frac { 3 }{ 2 } } }{ { \left( 6+\sqrt { 35 } \right) }^{ \frac { 3 }{ 2 } }-{ \left( 6-\sqrt { 35 } \right) }^{ \frac { 3 }{ 2 } } } =\frac { a }{ b } \]

If \(a\) and \(b\) coprime positive integers, what is \(a+b\)?

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