Task management for open source companies

Hi fellow HNers. We're currently using GitHub as our main task management resource but it's starting to grow on us since we have non-code tasks/non repository we'd like to keep progress on. The ideal system would have deep integration to GitHub as most of the work do comes from there, and we don't want to have the annoyance of two task management systems. (like if we "import" a ticket from GitHub any progress there is updated in our system and vice versa)