The modern Intel/AMD CPUs have distinct ALUs (arithmetic-logic units, where additions and other integer operations are done; usually between 4 ALUs and 8 ALUs in recent CPUs) and AGUs (address generation units, where the complex addressing modes used in load/store/LEA are computed; usually 3 to 5 AGUs in recent CPUs).

Modern CPUs can execute up to between 6 and 10 instructions within a clock cycle, and up to between 3 and 5 of those may be load and store instructions.

So they have a set of execution units that allow the concurrent execution of a typical mix of instructions. Because a large fraction of the instructions generate load or store micro-operations, there are dedicated units for address computation, to not interfere with other concurrent operations.