Determine which integer(s) from the set $S: \{-18, 2, 15, 20\}$ will make the inequality $\frac{5}{6} m - 4 < \frac{1}{3} m + 5$ false.
A$S: \{-18, 2, 15\}$
B$S: \{-18, 2\}$
C$S: \{15\}$
D$S: \{20\}$
A$S: \{-18, 2, 15\}$
B$S: \{-18, 2\}$
C$S: \{15\}$
D$S: \{20\}$