JBMO-SL 2010 A3

Find all pairs $(x, y)$ of real numbers such that $|x|+|y|=1340$ and $x^{3}+y^{3}+2010 x y=670^{3}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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(-670, -670), (1005, -335), (-335, 1005)

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