\[ \large \left\lfloor { x }^{ 2 }-1 \right\rfloor +\left\lceil { x }^{ 2 }-4 \right\rceil +\{ { x }^{ 3 }+1\} ={ x }^{ 2 } \]

find the number of solutions to the above equation.

**Notation**: \(\{\cdot \}\) denotes the fractional part function.

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