Floors and Fraction

Algebra Level 5

$x + \dfrac {2017}{x} = \lfloor x \rfloor + \dfrac {2017}{\lfloor x \rfloor}$ If the sum of all non-integer real solutions $x$ to the above expression can be represented as $\frac{a}{b}$ , where $a$ and $b$ are coprime integers and $b$ is positive, find $a+b$ .