ABC Financial Services Sent letter to cancel membership, but they continue to try to bill me!! Internet

A few weeks ago my health club decided to sell one of their locations (the one closest to me), and so I decided to cancel my membership.  I called ABC Financial who informed me that I had to mail them a letter in order to cancel.  I didn't have to mail them a letter in order to join, so this was obviously just a way for them to put me through more trouble than they hoped I thought it was worth.  

While on the phone, the lady I was speaking with told me I would have to pay the next month's membership since we were a few days into it.  I explained to her that the club had made significant changes that voided the contract I was in, and she tried at least five times to convince me otherwise.  Once she realized it was a fruitless endeavor, she told me all I had to do was mail in a letter postmarked by August 18th and that would be sufficient to cancel my membership.

I did so, didn't hear from them for a while, and assumed that all was well.  Today (on Sunday the 28th), I get an email from them stating that I owe them $65.  Of course, they can send me an email on Sunday but their phone lines aren't open.  I plan on calling them back tomorrow and making sure they realize I sent my letter; however, there are other people on this site to whom the same thing happened and ABC Financial Services claimed they didn't get the letter at all and continued to harass them for the money.

If they claim the same thing with me, I'm not sure what the next step to take would be.  I haven't really had problems with health club billing before as it seems to be pretty straightforward most of the time.  Someone please let me know what I should do should they not resolve this situation amicably.  Thank you.