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Find the number of real solutions (x,y,z)(x,y,z)(x,y,z) of
{(x+y)3=z(y+z)3=x(z+x)3=y \begin{cases} (x+y)^{3}=z \\ (y+z)^{3}=x \\ (z+x)^{3}=y \end{cases} ⎩⎪⎨⎪⎧(x+y)3=z(y+z)3=x(z+x)3=y
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