Inspired by Brian Charlesworth

Algebra Level 4

\[\large{\sqrt [ 16 ]{ 1416317954-\frac { 1 }{ 1416317954-\frac { 1 }{ 1416317954-\frac { 1 }{ ...... } } } } =a+\sqrt { b } }\]

If above given question can be expressed in the form of two integers \(a\) and \(b\) such that \(b\) is square free. Find \(a+b\).

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