"Thanks, but no." makes no sense to me. I'm not fluent english speaker and perhaps I don't know this english expression. Could somebody please explain me with other words "Дякую, але ні." ? Thank you!
This phrase might make sense if you were speaking to an insistent salesman who won't take "no" for an answer. :) My guess is after you have already said "No thank you", this might be your second response.
It's basically just 'no thanks' but swapped around. Imagine it as 'thanks, but I'm fine'.
I'm getting such Polish vibes here, still getting surprised by it. That's what being a part of Poland-Lithuania for half a millenia does to you I suppose.