Expanding the left side:
(7m+6)(6-7m)
= 7m(6) + 7m(-7m) + 6(6) + 6(-7m)
= 42m - 49m^2 + 36 - 42m
= -49m^2 + 36

Expanding the right side:
36 - m(m+1)
= 36 - m^2 -m

Now, equating the two sides:
-49m^2 + 36 = 36 - m^2 - m

Combining like terms:
-49m^2 + 36 = 36 - m^2 - m
-49m^2 + m^2 + m = 0
-48m^2 + m = 0
m(-48m + 1) = 0

Therefore, the possible values for m are:
m = 0 or m = 1/48