I do not know of any 11kV soft starters, only 3.3kV. You have done well to find 6.6kV. If you need to do a reduced voltage start, looks like your best bet will be a closed Korndorffer autotransformer type. Expensive I know. An autotransformer can be superior to a soft start because it gives you the most motor torque per amp of line current.
Another possibility might be, if you have not committed to a motor type yet and if one is available in your speed/power, to use a slipring type wound rotor induction motor with an automatically controlled stepping resistor for the rotor winding. Start with maximum rotor resistance to give high torque/low starting current and progressively remove resistance to provide torque as the motor accelerates.
Both I guess are "old technology" and expensive. The solution proposed by electrageek would be OK if the motor was Delta but most MV motors are star.
Obtain (from the power or lines company) the source fault level and X/R ratio to the point of common coupling (i.e. the point to which others connect to the power system) then calculate the source resistance and reactance. Work out what your starting current will be and then calculate the voltage dip as described by electrogeek. Don't forget that the motor starting current is at a low power factor (about 0.2) and you MUST take this into consideration when you calculate the voltage dip. The motor vendor will be able to provide all the necessary motor data such as full load amps, locked rotor current and the starting power factor. This voltage dip is the one that is important as it affects other users, not just your plant. It is limited by what the power company or lines company will let you do. Typically this might be up to 3% say 9 times per hour, depends on country. It is a "relative" dip i.e. voltage falls by x during the impact load.
The allowable dip you can cause in the plant itself is up to you. What can you live with? If you take in supply at HV, then you will have an HV/11kV transformer, cables etc. Work out the voltage dip (as described by electrageek). Most of the dip will be across your HV/11kV transformer and you can work out what this will be (as a check) using the transformer regulation formula given in the J&P transformer book.
You should also think about doing a motor starting study. To do this you will need motor and driven equipment torque-speed curves and inertias and also the motor current-speed curve.
Regards