Dirty Algebra

Geometry Level 3

${ a }\sqrt { 1-{ a }^{ 2 } } =\frac { 1 }{ \sqrt { 6 } }$

Given that the equation above is fulfilled for $0<a<1$ , find ${ a }^{ 6 }+{ \left( 1-{ a }^{ 2 } \right) }^{ 3 }$ .