If $(x,y,z)$ is the point on the sphere $x^2+y^2+z^2=4$ that is closest to the point $(3,1,-1),$ then $x+y+z=$

a$.-\frac{1}{\sqrt[\phantom{2}]{11}}$

b$.4$

c$.-\frac{5}{\sqrt[\phantom{2}]{11}}$

d$.\frac{6}{\sqrt[\phantom{2}]{11}}$

e$.\frac{3}{\sqrt[\phantom{2}]{11}}$