How about $x+\sqrt[3]2 y+\sqrt[3]4 z$, $x+\omega\sqrt[3]2 y+\omega^2\sqrt[3]4 z$ and $x+\omega^2\sqrt[3]2 y+\omega\sqrt[3]4 z$ where $\omega=\exp(2\pi i/3)$?
Robin Chapman
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