SMO 2005 Senior Round 1 Question 16

Consider the function $f(x)=\frac1{3^x+\sqrt3}$. Find the value of
$$\sqrt3\,[f(-5)+f(-4)+f(-3)+f(-2)+f(-1)+f(0)+f(1)+f(2)+f(3)+f(4)+f(5)+f(6)].$$