Answer
The function is neither even nor odd.
Work Step by Step
$f(x)$ is even if $f(-x)=f(x).$ If so, it is symmetric relative to the y-axis.
$f(x)$ is odd if $f(-x)=-f(x).$ If so, it is symmetric relative to the origin.
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Replace x with $-x$ and check the result:
$f(-x)=1-(-x)^{1/3}=1-(-x^{1/3})=1+x^{1/3},$
which is neither $f(x)$ nor $-f(x)$.
The function is neither even nor odd.
