Isn't Familiar! Part III

Algebra Level 5

\[\left\{\begin{matrix} 4x^3-3xy=9x+\sqrt{(x+3)^3} & & \\ 3x^2-2y+1=7x-2\sqrt{x+1} & & \end{matrix}\right.\]

How many pairs of \((x,y)\) satisfy the system of equation above?

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