If \( x=\sqrt[3]{\sqrt{2}+1}-\sqrt[3]{\sqrt{2}-1} \), show that \( x^{3}+3 x-2=0 \)

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If \( x=\sqrt[3]{\sqrt{2}+1}-\sqrt[3]{\sqrt{2}-1} \), show that \( x^{3}+3 x-2=0 \)
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