Last week I went abroad, and my FP6 with eOS3.6 refused to roam with my normal Congstar SIM, i.e. internet was dead. After much troubleshooting, eOS seems to pick a non-working APN (Access Point Name) for your SIM abroad, but this here seems to help:
Settings > Network & Internet > Internet > (your SIM, e.g. Congstar) > Settings (Gear symbol) > Access Point Name (APNs) > Actions (Three Vertical Dots symbol) > “Reset to Default”
Dunno if someone else also encountered this, but I wanted to share this here.