# Egyptian Floor Fractions

Algebra Level 5

$$x$$ is a real number that satisfies $\dfrac{1}{\lfloor x \rfloor}=\dfrac{1}{\lfloor 2x \rfloor}+\dfrac{1}{\lfloor 3x \rfloor}+\dfrac{1}{\lfloor 5x \rfloor}$

Let the largest possible value of $$x$$ be $$M$$, and the smallest possible value of $$x$$ be $$m$$. If $$M+m$$ can be expressed as $$\dfrac{p}{q}$$ for positive coprime integers $$p,q$$, then what is $$p+q$$?

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