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05AB1E, 51 38 bytes
-13 bytes thanks to Kevin Cruijssen!
',ð:#ʒ'-м€.ïß}D.ï≠ÅÏ'-¡¤LsнUʒX&lt;›]˜Ùg1M

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Explanation
                                      // Implicitly Read in multiline string 
 ',ð:#                                //Swap commas with spaces and split on spaces
      ʒ'-м€.ïß}                       //Filter list to only those with - removed are numbers
               D                      //Duplicate
                .ï≠ÅÏ                 //For all the ones that aren't numbers (so the ranges)
                    '-¡               //Split on dashes
                       ¤L             //Generate list from 1 to the highest number
                         sнU          //Stick the lower number in the variable U
 ʒ®&lt;›]                                //Filter out numbers less than the lower number
      ˜                               //deep flatten
        Ùg                            //Uniquify and count 
          1M                          //Push 1 then output the largest number in the stack