ILL 1990 Problem 53

Find the real solution(s) for the system of equations $\begin{cases}x^3+y^3 &=1x^5+y^5 &=1\end{cases}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.