A lead acid battery has a voltage of 1.9 to 2.2 Volts per cell. Having six cells, this produces a terminal voltage of 11.4 to 13.2 Volts for a fully charged battery with no load. The exact voltage depends on the concentration of the battery acid.
So, your battery at 11.5 is at the very bottom of the range and therefore marginal. If it's a sealed one, there isn't much you can do.
If the battery is fully charged, then it should turn over the starter motor even if it is only 11.5 Volts. The reason you oly hear a click could be due to a faulty starter solenoid. One way to check is to measure the voltage as you push the starter button. The voltage drop would be several volts if the starter motor is indeed trying to turn over. If the voltage drops only slightly, maybe 1 volt, then my bet is on the starter solenoid.