AUSTRIAN-POLISH 1993 Problem 5

Solve in real numbers the system $\begin{cases} x^3 + y = 3x + 4 2y^3 + z = 6y + 6 3z^3 + x = 9z + 8\end{cases}$

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.