\[\begin{cases} x+ \lfloor y \rfloor+ \left \{ z \right \}=1.1\\ \lfloor x \rfloor+ \left \{ y \right \}+z=2.2 \\ \left \{ x \right \}+y+\lfloor z \rfloor=3.3 \end{cases} \]

Find the solution to the system of equations and submit your answer as \(x+y+z\).

**Notations**:

- \( \lfloor \cdot \rfloor \) denotes the floor function.
- \( \lceil \cdot \rceil \) denotes the ceiling function.
- \( \{ \cdot \} \) denotes the fractional part function.

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