Does cutting a 'v' in my nail cure an ingrown toenail?

No.  The nail is formed by the matrix at the base.  Cutting a notch or ‘v’ in the tip effectively does nothing to change the shape or growth of the nail into your skin.

Dr. Craig H. Thomajan, DPM, FACFAS, FAENS
Founder and Managing Partner of Austin Foot and Ankle Specialists