Floors Are Negligible

Algebra Level 5

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

Find the sum of all non-integer real numbers \(x\) that satisfy the equation above.

\[\] Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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