Answer
$x=2$
Work Step by Step
We solve:
$\sqrt{1+x^{3}}=3$
$(\sqrt{1+x^{3}})^2=3^2$
$1+x^{3}=9$
$x^{3}=9-1$
$x^{3}=8$
$x=\sqrt[3]{8}$
$x=2$
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