Common Emitter resistors interactions
It's not so much that they affect the gain, but the fact that this change to R1 takes the transistor outside its linear operating region.

With a pair of 11K resistors for R1 and R2 you're trying to bias the base at 2.5V.

With a typical VBE of about 0.6V that means you're looking for 1.9V across RE, which in turn means an emitter current of about 4mA.

However, to get that 4mA flowing through RL to get to RE you would need to have a voltage drop of 18V across RL which you can't get anywhere near with a 5V supply.

The result is that the transistor becomes fully saturated trying to achieve that emitter current and in that state an increase in base current has very little effect on the collector current and hence very little effect on the voltage at the collector. The result is that the circuit no longer gives you the gain you want.