Solve for y, p, z, a
\left\{\begin{matrix}\\y=\sqrt[3]{z}\text{, }z=\left(\sqrt[3]{p+1}+\sqrt[3]{p-1}\right)^{3}\left(p+1\right)^{3\sqrt[3]{p-1}-1}\text{, }p>-1\text{, }a=z\text{, }&\text{unconditionally}\\y=\sqrt[3]{z}\text{, }z=\left(\sqrt[3]{p+1}+\sqrt[3]{p-1}\right)^{3}\left(p+1\right)^{3\sqrt[3]{p-1}-1}\text{, }p\in \mathrm{R}\text{, }a=z\text{, }&p<-1\text{ and }Denominator(3\sqrt[3]{p-1})\text{bmod}2=1\text{ and }Denominator(-\sqrt[3]{p-1}+\frac{1}{3})\text{bmod}2=1\end{matrix}\right.
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