Are you sure it's all about cutting and soldering ? I've made my own strip consisted of 8 LEDs, so I had to put 3 resistors there (each for every sub-string of LEDs: 1 for 2LEDs and 2 for 2 subsx3LEDs), so if you cut my strip it wouldn't work at all, but if you cut in appropriate places there's a chance it would work, but one sub-string would shine brighter (like last two LEDs for example)

It's all about wires inside and maths: how many resistors is put for which LEDs - unless you don't know it, you can't be right.