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{x3−xyz=2y3−xyz=6z3−xyz=20 \begin{cases} x^3-xyz=2 \\ y^3-xyz =6 \\ z^3-xyz = 20 \end{cases} ⎩⎪⎨⎪⎧x3−xyz=2y3−xyz=6z3−xyz=20
If x,yx,yx,y and zzz are real solutions satisfying the system of equations above, and the maximum value of x3+y3+z3x^3+y^3+z^3 x3+y3+z3 is equal to mn \dfrac mnnm, where mmm and nnn are coprime positive integers, find m+nm+nm+n.
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