How to Carry forward tickets to next sprint

What is the best way to carry forward the tickets to next sprint? Here is the scenario I had recently with one of my scrum team:

• There are 3 tickets in the current sprint 1 and we completed all of them and achieved committed work 3X3 = 9 story points and due to some dependencies with the upcoming new sprint 2 you will be not able to release 2 tickets (2X3 = 6 points).
• When the new sprint 2 is started you have 3 new tickets – Do we need to include those two left out tickets from sprint 1 as they are not released? Also if we include the story points will be calculated automatically to the board? Is this is the right approach we follow on scrum teams? Any thoughts?

According to what you are saying those two tickets are done but there are some pending dependencies. If they are done, then they meet the "definition of done" and should not be included in the next sprint because there are no work to do, although they have not been released. Otherwise it is that they do not meet the definition of done, therefore there is still work to be done, so in the sprint planning meeting you must define the new sprint goal and how to carry it out by estimating each new sprint backlog item including the work pending in this two tickets (which can be defined in subtasks of the main task to solve these dependencies).