Eleven cents per minute is already a low rate, and the honest answer is that even if InmateAid could shave something off that number, the savings would likely not cover the monthly line rental fee.
Here is the math. InmateAid's phone line runs $19.95 per month. To break even on that cost at $0.11 per minute, you would need to save at least $19.95 in per-minute reductions each month. If the best available rate at your facility is, say, $0.06 per minute, the savings of $0.05 per minute would require 399 minutes of calls per month just to break even on the line fee. That is a lot of phone time.
The service makes the most financial sense when the current rate is significantly higher, in the range of $0.21 per minute or above, where the per-call savings add up quickly and the monthly fee pays for itself within the first week of calls.
At $0.11 per minute, unless you are talking several hours every day, the math is probably not in your favor. InmateAid's goal is to save you money, not to sell you a service that costs you more than it saves. If you want a definitive answer for your specific facility, email aid@inmateaid.com with the facility name and your current number and the team will run the numbers and tell you straight whether it makes sense.