For all positive integers $n$ less than $385$, let
$a_n=\{\begin{array}{ll}5,& \text{if }n\text{ is divisible by }7\text{ and }11;\\ 7,& \text{if }n\text{ is divisible by }11\text{ and }5;\\ 11,& \text{if }n\text{ is divisible by }5\text{ and }7;\\ 0,& \text{otherwise}.\end{array}$

Calculate ${\sum }_{n=1}^{384}{a}_n$.