LDR will have a generic frequency response, which will peak at likely something in the middle of the visible spectrum. Do you have the spec sheet for your LDR? The LDR response may drop off rapidly away from its peak response. If the laser frequency is not close to the LDR peak then you may get poor or no response. You can compare LDR resistance range by using a strong incandecent light source, which has a broad spectrum.
Ciao, Tim