How to convert Third Octave data into single SPL quantity
Make sure that you are trying to compare same quantities, i.e. not $SEL$ with $L_{eq,C}$.
If third-octave levels were not measured with any kind of weighting and you are trying to calculate $L_{eq,A}$ for example, then you must apply corrections.
For each band calculate the anti-logarithm using the formula: $p_i=10^{L_i/10}$ (for example for $54.3 \mathrm{dB}$ that would be $218776.2$).
Sum all values you obtained in previous step and calculate the total level as: $10\log_{10}\left(\sum p_i\right)$.


That will produce exact result - tested second ago on some data from SLM.