It sounds a bit unnatural to me. You are relating something from the past, but then at the same time you are using a ...."either... or ...." construct. Because it happened in the past, you *should* remember and say which ONE action you took. This is where it sounds a bit strange. For it to work as you wrote, you really need to drop the 'either' at a minimum. It is more natural without it. For instance: "I didn't know the exact Persian equavalent of the proverb. I had to try my luck at surfing the Net or looking it up in a dictionary."

That looks perfect to me. Well done!