Floors Are Negligible

Algebra Level 5

x+2016x=x+2016x\large x+\dfrac{2016}{x}=\lfloor x\rfloor+\dfrac{2016}{\lfloor x\rfloor}

Find the sum of all non-integer real numbers xx that satisfy the equation above.

Notation: \lfloor \cdot \rfloor denotes the floor function.

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