No such county, city or town shall require a license or impose a license tax for the operation of any such motor vehicle for which a similar license is imposed or tax levied by the county, city or town of which the owner or operator of the motor vehicle is a resident, except that such license may be required and such license tax imposed by any such county, city, or town for the operation of any such motor vehicle if the owner, lessee, or operator thereof maintains a taxicab stand or otherwise solicits business within such county, city, or town; nor, except as herein expressly authorized, shall more than one county, city or town impose any such license fee or tax on the same vehicle. This article shall not be construed to apply to common carriers of persons operating as public carriers by authority of the Department of Motor Vehicles or under a franchise granted by any county, city, or town.