Having fun with exponents?

Algebra Level 4

\[\Large {\left(\sqrt[7]{{\left(\sqrt[7x]{7^x}\right)}^{\sqrt[7x]{7x^7}}}\right)}^{x} = {\left({\left(7^x\right)}^{\sqrt[x]{x}}\right)}^{\left(7^x\right)}\]

Find the sum of all real values of \(x\) satisfying the real equation above.

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


Why don't you have Fun with exponents?
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