Solving $\sqrt[3]{\sqrt {x-1} - 2} = 1-\sqrt[3]{9-\sqrt{x-1}}$ with symmetric polynomials

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I need to solve the following with symmetric polynomials, but I do not understand what to do here. $$\sqrt[3]{\sqrt {x-1} - 2} = 1-\sqrt[3]{9-\sqrt{x-1}}$$