Maximise it

Algebra Level pending

Find the maximum value of \[{ a }^{ 2 }{ +b }^{ 2 }+{ c }^{ 2 }+a+b+c\] subject to \[\begin{cases} a\ge -1,b\ge -1, c\ge -1 \\ { a }^{ 3 }{ +b }^{ 3 }+{ c }^{ 3 }=1 \end{cases} \]

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