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 \({ a }^{ 6 }+{ \left( 1-{ a }^{ 2 } \right) }^{ 3 }\).

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