Why isn't my operator override working on structs?

I'm trying to make a custom container to use as a dict key, so I can index values by an int and string instead of by one key. The intended usage is pretty simple:

 public class CalendarKey
 {
     public int myDayOfYear;
     public TimeOfDay myTimeOfDay;
 }
 
     public void TestStructDict()
     {
         CalendarKey keyA = new CalendarKey();
         keyA.myDayOfYear = 1;
         keyA.myTimeOfDay = TimeOfDay.Afternoon;
 
         CalendarKey keyB = new CalendarKey();
         keyB.myDayOfYear = 1;
         keyB.myTimeOfDay = TimeOfDay.Afternoon;
 
         Dictionary<CalendarKey, string> testDict = new Dictionary<CalendarKey, string>();
         testDict.Add(keyA, "Key A");
         Debug.Log(testDict[keyA]);
         Debug.Log(testDict[keyB]);
     }

My expectation is for testDict[keyA] and testDict[keyB] to return the same data, since structs are value types, not reference types, but testDict[keyB] returns a key not found exception. I thought this might mean that I need to manually add a comparison operator:

 public class CalendarKey
 {
     public int myDayOfYear;
     public TimeOfDay myTimeOfDay;
 
     public override bool Equals(object obj)
     {
         if (obj == null)
         {
             return false;
         }
 
         CalendarKey key = (CalendarKey)obj;
         if (key == null)
         {
             return false;
         }
 
         return myDayOfYear == key.myDayOfYear && myTimeOfDay == key.myTimeOfDay;
     }
 }

However, this has no effect, and the error persists- is it simply not possible (or at least recommended) to use structs as dict keys, or am I doing something else wrong here?