Tough to answer your questions without seeing the LLC agreement and your shareholder agreement. As you may know, some LLCs have classes of shares that vote and do not vote. There may also be delineations between who receives profits and when. All of this will have to reviewed by an attorney.
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.
Many operating agreements actually have provisions about the buy-sell aspects and in particular discuss whether discounts (minority or lack of marketability) should be applied (or not) to the valuation of a member's shares. Check there first to see if covered or not specifically because you may have your answer and the assertion of voting rights vs. non-voting rights may be of no consequence at all.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.
I agree with the other two answers. Understanding the operating agreement and articles of organization is critical. Valuation in these cases may be subject to negotiation if the key documents do not set the price. In such a negotiation there are many factors that affect the value including the limited market for selling and the lack of voting rights. Often the value will be determined by the return on investment produced by the stream of income, if any; sometimes the present value of what would be produced by future liquidation from the sale of the underlying assets will be the major factor in determining value, and present value is an assumed discount rate of interest which is also subject to negotiation. Good luck.
These comments do not constitute legal advice. They are general comments on the circumstances presented, and may not be applicable to your situation. For legal advice on which you may rely consult your own lawyer.