\[\Large \big({\sqrt[3]{x}}\big)^{x^3} = {x^{3\sqrt[3]{x}}}\]

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

If the answer is of the form \(\sqrt[8]{a}\), submit the value of \(a\).

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

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