We do use JIRA at the office and the problem with GTDing using tools like that is that it's not just your system, it's everybody else's on your team / at your company. Other people can go in easily and make changes to your tasks, assign new items to you and so on which I found to be a bad practice with GTD, which in turn is mostly about your internal and external commitments that you should make up, not others.
I hear you, however, and the best integration I can imagine is to be able to import a JIRA filter (such as assigned tickets or a custom filter) as a next action list such as @work or something into your GTD software. Unfortunately I don't know of any compatible app but since JIRA has an API and now they do have the JIRA Query Language maybe there is something out there that can be connected.
Again, be careful since these tasks can be created by others and they may or may not be next actions (they are more likely "stuff" that needs clarification rather than specific next actions) unless your Product Owner and/or Scrum Team is really good in GTD.
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