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{a3=a+1b3=b+1c3=c+1 \large { \begin{cases} a^3 = a + 1 \\ b^3 = b +1 \\ c^3 = c + 1 \end{cases}} ⎩⎪⎪⎨⎪⎪⎧a3=a+1b3=b+1c3=c+1
If a,ba,ba,b and ccc are distinct numbers satisfying the system of equations above, find a3+b3+c3a^3 + b^3 + c^3 a3+b3+c3.
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