Yes, an out-of-state traffic ticket will normally go on your Missouri driving record and thus could affect your car insurance rates.
Your home state of Missouri, as well as Mississippi, the state where you received your ticket, are members of an interstate agreement called the Driver License Compact (DLC).
With the DLC, if you are convicted of a moving violation in a member state, they will notify your home state's licensing agency, and then it depends upon your state's laws if the offense will go on your driving record or not. The Department of Revenue (DOR) is the keeper of Missouri driving records.
The assessed point value on your motor vehicle record (MVR) will be determined by the Missouri violation conviction code, not Mississippi's. Speeding offenses in Missouri come with a point value of two or three depending upon the particulars of your speeding violation.
As for your auto insurance rates, if you are convicted of this Mississippi speeding violation (by simply paying your fine), it will be seen if by your car insurance company when they next pull your MVR, and could affect your rates.
Driving records are normally looked at every renewal period (though some companies pull it less often), and when you apply for car insurance (the inception of a new policy).
So, at your next renewal period the out-of-state violation will be known to your auto insurance provider, which may then cause your rates to rise depending upon the rating system of your carrier.
If this is the only traffic violation on your driving record, then it may not cause you to be surcharged by your insurer. You may, however, lose a good driver discount because of the ticket, and that would cause your premium to be higher. (See "Tickets that don't raise your insurance rates.")
Or if you already have other violations on your record and this one added to it will certainly raise your rates because you appear to be more of a risk to the car insurance company.