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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