Simplifying the radicals

Algebra Level 3

The value of SS is an integer II. Enter the value of II.

S=41+2925292415S=\sqrt[5] {41+29\sqrt {2}}-\sqrt[5] {29\sqrt {2}-41}

You may not use a calculator.

Assumptions\textbf{Assumptions}

Consider a5\sqrt[5] {a} to be the principal fifth root of a aRa \ \forall a \in \mathbb{R}.

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