# Sir Surds

Algebra Level 4

$\LARGE {\left(\sqrt[\dfrac{x^5}{5}]{\sqrt[\dfrac{1}{5x^5}]{{\left(5^{\sqrt{5x}}\right)}^{x^5}}}\right)}^{5x} = 5^{\sqrt[5]{5x^5}}$

Find the real value of $$x$$ satisfying the real equation above.

The answer is of the form $$5^{-\dfrac{a}{b}}$$, where $$a$$ and $$b$$ are co-prime positive integers, then what is the value of $$a + b$$?

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

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