If the solution of the equation
$\sqrt { { x }^{ 4 }-4x-16 } =2-x$
can be written as $x=a\sqrt { b }$ such that $a$ and $b$ are coprimes, then the correct value of $a+b$ is $\text{\_\_\_\_\_\_\_\_\_\_}$.

Source: Adapted from 1985's Lomonosov Moscow State University physics course admission exam.

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