How can I get gum off of my rose gold necklace that got stuck on it in the washer?

I washed a pack of chewing gum with a load of laundry by accident. It just so happened that my necklace was also tucked into one of my pockets. So now there's dried gum stuck in the chain and I can't get it out. I'm really upset and I don't know what to do about it, so I haven't been messing with the necklace much, This happened a few months ago, I know I should've tried to get the gum out sooner, but I was just too upset. My step mother gave it to me and she's very sick so I'd like to be able to wear it.. If you have any tips on how to get the gum out or on how to clean thenecklace I would really appreciate it. & unfortunately I don't have the money to take it to the jewelers to get it cleaned.