After some testing I found an easy way to backup tab sets links using a free web crawler named WebCopy. I am leaving here a mini tutorial of the steps I've followed:
Download WebCopy
New project
Website:
Forms and Passwords
Passwords
Log in using web browser
Ok
Project
Project Properties
General
Uncheck "Download all resources"
Copy
Login with browser
Copy
Tools
Website Links
Show External
Filter: exclude urls with "pinboard" (optional)
Select all
Export to csv
Open csv
Sort
Delete urls with "pinboard" (if not done before)
Delete urls starting with "uri"