Evaluate the line integral in Stokes' Theorem to evaluate the surface integral ${}_S(gradF)*ndS.$ Assume that $n$ points in an upward direction. $F=($:$x+y,y+z,z+x$:$)$;$S$ is the tilted disk enclosed by $r(t)=($:$5cost,6sint,\sqrt[\phantom{2}]{11}cost$:$).$

Find the value of the surface integral.

${}_S(gradF)*ndS=$

$($Type an exact answer, using $$ as needed.$)$