Since decibels are in logarithmic space, multiplication becomes addition and division becomes subtraction. Hence, the RATIO of signal level to noise level is in power space (i.e. Watts), so becomes a simple subtraction of signal level - noise level.
For the example, -65 dBm -65 dBm = 0 dB, which of course is unusable. In your example, your signal level is equal to your noise level, so your receiver will not be able to distinguish the desired signal from the background noise.
You typically want noise to be -90 dBm or lower, depending on the environment, channel sizes, etc. Especially for the higher order 802.11n and 802.11ac rates, you want SNR to be as high as possible. MCS9 for an 80 MHz channel in 802.11ac typically requires at least an SNR of +37 dB, to keep things in perspective.