  We show that two Dehn surgeries on a knot $K$ never yield manifolds that are
homeomorphic as oriented manifolds if $V_K''(1)\neq 0$ or $V_K'''(1)\neq 0$. As
an application, we verify the cosmetic surgery conjecture for all knots with no
more than $11$ crossings except for three $10$-crossing knots and five
$11$-crossing knots. We also compute the finite type invariant of order $3$ for
two-bridge knots and Whitehead doubles, from which we prove several
nonexistence results of purely cosmetic surgery.
