Another option, beyond telling to turn off the radio (which you already tried and didn't work) and talking to the manager (as others have suggested):
Start whistling...very quetly... ;)
I actually had a situation at work where someone on another team listened to a radio, and it reverberated all through the area, wasn't quiet at all. She worked for HR dept which was/is out of control in all sorts of ways, so this was part of a larger pattern, but nevertheless highly distracting. I ended up making a special trip to their area, and calmly and politely telling her to please turn off the radio as the acoustics resulted in the sound traveling to my work area.
I also told her I hope she would agree that it would be best if we could find an agreement among ourselves than to get management involved, especially as this appeared to be a violation of company policy about courteous and respectful conduct and minimizing distractions in the workplace. I made sure our conversation is overheard by several of her colleagues sitting all around her. I ended by thanking her in advance for her understanding and expressing hope that we don't have to revisit the issue again. That took care of it.
This also reminds me of a colleague who listens to classical music in headphones, but then HUMMS the tunes so loud that you can hear it 3 cubicles over. I am pretty sure she doesn't hear herself doing it, or if she does, thinks she is quite a virtuoso hummer. She really leans into it, and humms like crazy (I believe Mozart in particular excites her).
When it got too much, I walked past her humming the tune loudly enough to guarantee she would get the idea. After a couple humm-by's, it got better. Now whenever I hear humming, I simply begin to humm back. Doesn't always help, but I get a kick out of it every time. Neither of us has confronted the other yet, so it's a bit of that shaky equilibrium of don't ask/don't tell.
I guess you could try the same (bring your headphones and start listening to music and humming to the tune). There is a risk it might upset your colleagues, but your excuse is that it's your only solution for coping with the distraction. If all (including appeals to management) fails -- earplugs. Good luck!