René van Bevern has a solution for using Computer Modern for
\mathcal and \sum along with the mathptmx package.Using his idea, I have a very similar solution for using the Latin Modern font family instead.
\SetMathAlphabet{\mathcal}{normal}{OMS}{lmsy}{m}{n}
\SetMathAlphabet{\mathcal}{bold}{OMS}{lmsy}{m}{n}
\SetSymbolFont{largesymbols}{normal}{OMX}{lmex}{m}{n}
\SetSymbolFont{largesymbols}{bold}{OMX}{lmex}{m}{n}
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