Find it again!

Algebra Level 3

\[\Large {{\left(x\sqrt[4]{x}\right)}^x = x^{x\sqrt[4]{x}}}\]

Given that \(x\, (\ne 1,0,-1)\) satisfies the equation above and \(x \) can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).


This is one part of the set Fun with exponents.
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