Step 1 :Luis collected 610 beads.
Step 2 :Annie collected 100 more beads than Luis, which is \(610 + 100 = 710\) beads.
Step 3 :We need to find out how many groups of ten beads Annie collected. This can be calculated by dividing the total number of beads Annie collected by 10.
Step 4 :So, \(710 \div 10 = 71\).
Step 5 :Final Answer: Annie collected \(\boxed{71}\) groups of ten beads.