Ceilings? Floors?

$$\left \lceil x \right \rceil + \left \lfloor x \right \rfloor + \left \{ x \right \} = 6$$

How many different values for $$x$$ are there?

Clarification:

• $$\left \lceil x \right \rceil$$ is the ceiling of $$x$$
• $$\left \lfloor x \right \rfloor$$ is the floor of $$x$$
• $$\left \{ x \right \}$$ is the fractional part of $$x$$
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