\[\left\lfloor \frac { x }{ 1! } \right\rfloor +\left\lfloor \frac { x }{ 2! } \right\rfloor +\left\lfloor \frac { x }{ 3! } \right\rfloor =224\]

Find the integer value of \(x\) that satisfies the equation above.

Note: \(\lfloor x \rfloor\) denotes the greatest integer that is smaller than or equal to \(x\).

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