
Simply put, there is NO IUPAC rule based on summing the locants despite what you may have been taught elsewhere!
However, to be honest, the sum idea works in most simpler cases (unfortunately). But, learning the "sum rule" typically means one doesn't take the time to learn the first point of difference rule which is required in several other situations. Therefore, it is recommended that you learn the first point of difference rule as you will probably need to learn it at some point anyway, and it really isn't any more difficult to learn!
Mathematically, it is summing a list of numbers versus comparing a list of numbers written in numerical order (which only requires kindergarden math !)
HINT:
Here are some examples of the application of the first point of difference rule to generate the correct name where the mythical "sum rule" fails:
Consider the following example (from an IUPAC nomenclature website):
If we were to sum, then the total from the first numbering scheme (left to right) 3 + 4 + 9= 16, the second scheme (right to left) 2 + 7 + 8 = 17 However, let's follow a logical method for identifying the first point of difference... 
As you will learn later, for cycloalkenes, the two carbon atoms in the alkene C=C must be numbered 1 and 2. Therefore scheme 1 is incorrect because this is not the case (since the C at "2" is not part of the alkene). Schemes 2 & 3 need to be distinguished based on the first point of difference rule:

©Dr. Ian Hunt, Department of Chemistry 