Let $a_n=\frac{11}{\sqrt[\phantom{2}]{n}+ln(n)}$ and $b_n=\frac{1}{\sqrt[\phantom{2}]{n}}.$ Calculate the following $limit.$

$(Givean$ exact answer. Use symbolic notation and fractions where needed. Enter DNE $if$ the $limit$ does not exist.$)$

$\underset{n}{lim}\frac{a_n}{b_n}=$