Small looking integrals have really big solutions

Calculus Level 3

\[ \large \int _{ 0 }^{ 1 }{ \frac { { ( 1 -16{ x }^{ \frac { 1 }{ 4 } } ) }^{ 2 } }{ { ( { 2 }^{ 8 }\ x ) }^{ \frac { 7 }{ 8 } } } \, dx } \]

If the integral above can be written as \( \frac{a}{b} \) for positive coprime integers \(a, b \). Find \( a + b \).

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