Every nonzero complex number (including real numbers) has $n$ $n$-th roots in $\Bbb C$, if $n$ is a positive integer. That is, if $z\in\Bbb C$ and $z\ne0$, then the polynomial $X^n-z$ has $n$ distinct roots in $\Bbb C$.
In case $z$ is a positive real number, then among those $n$, one root is distinguished, namely the one that’s positive, and we write this root $z^{1/n}=\sqrt[n]z$, indifferently.
In case $z$ is a negative real number and $n$ is odd, that is, if $n=2k+1$ for $k\ge0$, then there’s a distinguished $n$-th root, namely the negative one, and we write it $z^{1/n}=\sqrt[n]z$, indifferently.
If anyone tries to tell you in either of the two above cases that $z^{1/n}\ne\sqrt[n]z$, that person is wrong. I admit that this is a matter of notation rather than of the underlying mathematics, but in my oh so many years of mathematics and mathematics teaching, I have never seen it claimed that the two are different.
When $n$ is not a positive integer, and in the second case when $n$ is an even integer, then of course all bets are off, and the ambiguity of the situation overcomes all attempts at pedagogical and notational clarity.