Individual Fractional Part of Roots!?

Algebra Level 2

\[ x^3-x^2-5x+1=0 \]

If the roots of the above equation are \(\alpha\), \(\beta\), and \(\gamma\), find the value of \(\{\alpha\}+\{\beta\}+\{\gamma\},\) where \(\{ \cdot \}\) denotes the fractional part function.

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