Multiple exhibitor equation

Is there a way to get the result for this value of x?

x ^ x ^ (x ^ (1/6) / 6) == Sqrt[2^9]^ (2 * Sqrt[2]) ^ (2/3 + 2 * Sqrt[2])

I have tried Solve, FindInstance and I did not have a solution

I have tried this:

Solve[X^x^(x^(1/6)/6)==Sqrt[X^x^(x^(1/6)/6)==Sqrt[x^x^(x^(1/6)/6)==Sqrt[x^x^(x^(1/6)/6)==Sqrt[2^9]^ (2 * Sqrt[2]) ^ (2/3 + 2 * Sqrt[2]) {X}]