Centre of LOVE 2

A quadrilateral $LOVE$ has the coordinates of the vertices as $L=(2,5)$ , $O=(6,\frac{71}{12})$ , $V=(5,1)$ and $E=(0,\frac{17}{12})$ . Find the coordinates of the meeting point of its diagonals.

If the required coordinates can be written as $(\frac{a}{b},\frac{c}{d})$ , where $\gcd(a,b)=1$ and $\gcd(c,d)=1$ , find the value of $a+b+c+d$ .