Mazal tov on your upcoming wedding!

The halacha states that immersion is valid if nails are clean (no dirt underneath) and without hangnails. There is a longstanding custom to shorten them in order to make cleaning easier. Specifically, the nails should not be longer than the top of the finger, in other words the nails would not be visible when looking at your hands from the side of your palm. However, you may immerse with long nails on condition that are filed smooth, with no hangnails, and they can be perfectly cleaned despite their length.