Is this possible?

If

\(a+b=4\)

\(\sqrt [ 3 ]{ a } +b=5\)

\(a+\sqrt [ 3 ]{ b } =6\)

and \({ a }^{ \frac { 2 }{ 3 } }+{ b }^{ \frac { 2 }{ 3 } }=x\) is true,

Find \(\left\lfloor 1000x \right\rfloor \)

If you think there is no solution, enter 567.

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