can pins 3 and 11 on the 556 timer use the same capacitor to ground?
Yes, in many circuits the two control pins on a '556' timer can be connected, and a single capacitor can be used to "decouple" both of them.   
This does not apply in applications when the control pin is being fed with an external signal (unless it is the same signal for each timer). Some applications do connect external signals here but most applications don't.


This pin connects to the top tap of the reference divider used by the internal "window comparator". In son=me cases applications may want to adjust this level by applying other  signals, but in many applications it is not connected to an external "signal" and may then be joined to other similar control terminals.

Below is a block diagram of a single 555 timer - the 556 is essentially two of these timers in one package. A '555' datasheet can be found here

The control terminal, pin 5, connects to a point on a resistive voltage divider made of 3 equal valued resistors which are connected between Vcc and ground. So, Vcontrol = 2/3 Vcc. If Vcontrol is not modified by the application circuit then it may be connnected to another Vcontrol pin, as above. 

In a low noise system it MAY be possible to not connect a capacitor to Vcontrol. If Vcc is relatively noise free then the divider will be notionally noise free as well. However, any noise on vcc will appear on both reference points on the divider and will affect the upper and lower switching thresholds.  Adding a capacitor from control pin to ground "decouples" any noise. This capacitor can be shared between multiple control pins. 

You do not strictly need to increase the capacitor value when commoning control pins, although it does not hurt to do so.
 The capacitor and resistors form a low pass noise filter with time constant of roughly 2/3 x R x C (due to 2R to ground and R to Vcc the resistance looks like 2/3R.)
 Commoning two pins with the same capacitor will halve the time constant and make the filter "somewhat worse".
 Any system that works OK with 2 x C here but is not acceptable with  1 x C here was too marginal in the first case and should have had a larger C value initially.