Sorry, but all three types of VMC (a,g,or l - even more if you're a 3+engined type!) are dependent on a bit more than the simple yawing moment balance you mention.
Vmca is affected by the allowance of banking into the live engine, as is Vmcl. Both may also be influenced by the 'dynbamic Vmc' requirement, or by roll control requirements to turn into/outof the dead engine.
Vmcg is heavily influenced by all kinds of undercarriage dynamics, in addition to being heavily dependent on pilot reactions (and crosswind, though we usually cough and move on after mentioning that).
The yawing moment balance is good for giving a first approximation, but it isn't the whole story.