Let $$ABC$$ be an isosceles triangle with sides $$13$$, $$13$$ and $$10$$. The tangents to the incircle, drawn parallel to the sides, intersect the sides in points $$D$$, $$E$$, $$F$$, $$G$$, $$H$$, $$K$$ which form a hexagon. If the area of the hexagon $$DEFGHK$$ is $$m+\frac{n}{l}$$, where $$m,n,l$$ are positive integers with $$n<l$$ and $$\gcd(n,l)=1$$, what is $$m+n+l$$?