We demonstrate experimentally the dual beam optical drive of an interconnect-free 2-input, 2-output 1-bit adder implemented inside a single gold plasmonic cavity, focused ion milled in an ultrathin single crystalline gold microplate. To obtain this result, we have set a coherent 2-beam excitation scheme up that allows us to independently and arbitrarily choose the intensity, polarization, and relative phase shift of two femtosecond-pulsed laser spots. The spots are focused on any chosen location of the micrometer-sized plasmonic cavity. The nonlinear photoluminescence (NPL) response of the cavity encodes the Boolean output, while the Boolean inputs are borne by the linear polarizations of the excitation. A generic map analysis tool is developed to pinpoint the realized Boolean functions and to assess their robustness. This tool is used to demonstrate the experimental implementation of the elusive XOR gate and its combination with an AND gate in the same cavity to perform the full 1-bit adder. The analysis of 160,000 instances of the 1-bit adder clearly shows the soundness of our approach and reveals some underlying mechanistic features of the remotely generated NPL. These results establish the first practical step of a general approach to cascade-free all-optical arithmetic and logic units.