Graphing can fool you 2
\[\large \left \lceil x^2 \right \rceil = \lfloor 2|x| \rfloor \]
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 \(x\).