A hexagon is inscribed in a circle of radius $r$. Two of its sides have length 1, another two have length 2, and the last two have length 3. If $r$ is a root of $ax^{3}+bx^{2}+cx+d=0$, where $|a|, |c|$ and $|d|$ are prime numbers, then find the value of $|a|+|b|+|c|+|d|$.