Creative Question I

Algebra Level 2

\[\large \sqrt[3]{x+\sqrt[3]{x+\sqrt[3]{x+\cdots}}}\ =\ \sqrt[3]{x\ \sqrt[3]{x\ \sqrt[3]{x\ldots}}}\]

The non-zero solution \(x\) of the equation above can be written as \(\frac{\sqrt{a}+\sqrt{b}}{2},\) where \(a\) and \(b\) are positive integers.

What is \(a+b?\)

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