\[\large \dfrac{a^3+2}{b^2+1}+\dfrac{b^3+2}{c^2+1}+\dfrac{c^3+2}{a^2+1}\]

Given that \(\large 0\leq a,b,c\leq 1\). Let the maximum value of the expression above is \(A\). The sum of \(a,b\) and \(c\) when the equality holds is \(B\). Compute \(\large AB(A+B)\).

**Note**: You don't need to try \(a=b=c\). Because it isn't the answer.

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