Roots inside roots?

Algebra Level 4

\[\huge{\sqrt[{\sqrt[4]{4x}}]{{(x^4)}^{\sqrt[4]{x}}} = x^x}\]

Find the real value of \(x\) satisfying the equation above.

The answer is of the form \(a × \sqrt[4]{b}\), where \(a\) and \(b\) are integers, then what is \(a + b\)?

\(\text{Note}\):- Here \(x \neq 0,1\)

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