Determining the domain of a polynomial with rational exponents

I believe the issue here is the definition of negative numbers raised to rational powers that's used by Wolfram or your graphing software. A robust definition of exponentials that's used by most software because it generalises to complex numbers is: $$a^b := \exp({b\ln a}),$$ where $\exp x=e^x$, and in the case where $a$ is complex, $\ln$ is the principal logarithm. The issue now, is when you try to evaluate something like $(-1)^{2/3}$. If we use the definition we have $$(-1)^{2/3}=\exp\left(\frac23\ln(-1)\right),$$ which clearly makes no sense in $\mathbb R$ (the $\ln$ of a negative number is undefined). So to answer your question, the reason wolfram thinks $(-1)^{2/3}$ is undefined is because of the robust definition for exponentiation, which gives $(-1)^{2/3}$ as a complex number.