TTC & Fallopian Tube Blockage

Has anyone had luck while TTC with a blockage of their fallopian tube(s), without surgery or IVF? Husband and I have been trying for 11 months. I was having a lot of pain on my left side (what turned out to be acyst on my left ovary) and during exam the ultrasound showed signs of blockage in both tubes. Husband and I are talking risks and costs of helpful procedures, but no decision has be made yet. Has anyone been told they also had some type of blockage but still managed to conceive without the need for IVF or the invasive surgeries?