How to remove a dented lens filter?

My Nikon 18-105mm lens was dropped and the glass of the filter cracked and the rim got dented.
The damage is similar to this:

However there's also a dent on the rim of the filter.

I removed the broken glass and only the rim of the filter remains. It is stuck VERY tight. I have attempted to twist it off with a cloth and firm against a rubbery surface, however it won't budge.

I've read online about methods of removing dented filters, however most people suggest getting it professionally mended. I'm looking only for ways to repair it myself at this stage.

I've read about the threads on the filter and lens getting damaged, therefore I have not attempted any extreme methods as I'm fearful of damaging the lens threads when trying to remove the broken filter, therefore making it difficult to screw the new filter back on. Are they very delicate? How careful do I need to be in order not to ruin them?

Any suggestions would be much appreciated.

If the filter mount on the lens is not dented, you are very lucky.
since the broken glass has been removed you should be able to collapse or crush the damaged filter with a large pair of "channel lock pliers". Just be very careful not to touch the lens filter mount area and have someone hold the lens while your are doing this. Or you can just use the lens as is without a filter. Trying to unthread it could damage the lens threads since the filter is distorted and no longer round. If you are uncomfortable doing this, than send it out for repairs.
Precision Camera should be able to handle it.
http://www.precisioncamera.com/