Algebra with complex numbers

Let $m$ be the minimum value of $|z|$, where $z$ is a complex number such that

$$ |z-3i | + |z-4 | = 5. $$
Then $m$ can be written in the form $\dfrac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Find the value of $a+b$.

I cannot seem to get rid of the absolute values, making it impossible to solve this. Is it possible for someone to give me some help?

Thank you!