\[\large \left \lceil x^2 \right \rceil = \lfloor 2|x| \rfloor \]

There are \(m\) integral values and \(n\) ranges of values of \(x\) that satisfy the equation above. What is \(m+n\)?

**Bonus**: Find all these \(m\) integers and all the intervals of each of the \(n\) ranges of \(x\).

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