General rule is that you need at least 30" dish for any linear Ku satellites. Signal on these satellites is not as strong as Dish or Directv satellites so you need a bigger dish. I am not Dish Network expert, but its LNB is circular and T11 uses linear polarity.
Your best bet would be to get a separate dish and LNB for T11 (and if you want to fully enjoy everything Ku has to offer, invest in
motorized system).
Check out Fortec dishes and LNBs that
Sadoun is selling.