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 \(a+b\).