For complex number $u = a+bi$ and $v = c+di$ (where $i=\sqrt{-1}$), define the binary operation $u \otimes v = ac + bdi$.  
  
Suppose $z$ is a complex number such that $z\otimes z = z^{2}+40$. The original answer for $|z|$ is in the form $k\sqrt{m}$. Please find the value of $k + m$.

Let's think step by step and output the final answer within \boxed{}.
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