Answer
$(3m+11n)(2m+n)$
Work Step by Step
$6m^{2}+25mn+11n^{2}=$
...find factors of $ac$ with a sum of $b$.
($ac=66,\ b=25$)
$\left[\begin{array}{lll}
\text{Factors of 66} & \text{Sum of factors} & \\
2\text{ and }33 & 35 & \\
3\text{ and }22 & 25 & \text{ is what we need }
\end{array}\right]$
...use the factors you found to rewrite $bx$.
$=6m^{2}+3mn+22mn+11n^{2}$
...factor by grouping.
$=3m(2m+n)+11n(2n+n)$
...use the Distributive Property.
$=(3m+11n)(2m+n)$