I ask ESL and EFL learners to become better in speaking by listening with their heart. When someone speaks with you, when they share their personal information, consider thinking about how that person feels about the information they just shared. How would you feel if you were in their shoes? Make a comment about how you think they must be feeling as part of the conversation. That helps to establish a bond between you and your conversation partner. Focusing on that rather than on what the person thinks about your accent, is a better use of time.
What effect would this have on the person with whom you are speaking?