# Is this possible?

Number Theory Level 4

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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