diff --git a/doc/whatsnew/fragments/10435.false_positive b/doc/whatsnew/fragments/10435.false_positive
new file mode 100644
index 0000000000..0ad1a29cb0
--- /dev/null
+++ b/doc/whatsnew/fragments/10435.false_positive
@@ -0,0 +1,3 @@
+Add Enum dunder methods ``_generate_next_value_``, ``_missing_``, ``_numeric_repr_``, ``_add_alias_``, and ``_add_value_alias_`` to the list passed to ``--good-dunder-names``.
+
+Closes #10435
diff --git a/pylint/constants.py b/pylint/constants.py
index c48fe7af0e..6a2481913b 100644
--- a/pylint/constants.py
+++ b/pylint/constants.py
@@ -219,26 +219,31 @@ def _get_pylint_home() -> str:
         "__anext__": "Use anext built-in function",
     },
 }
-
-EXTRA_DUNDER_METHODS = [
-    "__new__",
-    "__subclasses__",
-    "__init_subclass__",
-    "__set_name__",
-    "__class_getitem__",
-    "__missing__",
-    "__exit__",
-    "__await__",
-    "__aexit__",
-    "__getnewargs_ex__",
-    "__getnewargs__",
-    "__getstate__",
-    "__index__",
-    "__setstate__",
-    "__reduce__",
-    "__reduce_ex__",
-    "__post_init__",  # part of `dataclasses` module
-]
+EXTRA_DUNDER_METHODS: dict[tuple[int, int], list[str]] = {
+    (0, 0): [
+        "__new__",
+        "__subclasses__",
+        "__init_subclass__",
+        "__set_name__",
+        "__class_getitem__",
+        "__missing__",
+        "__exit__",
+        "__await__",
+        "__aexit__",
+        "__getnewargs_ex__",
+        "__getnewargs__",
+        "__getstate__",
+        "__index__",
+        "__setstate__",
+        "__reduce__",
+        "__reduce_ex__",
+        "__post_init__",  # part of `dataclasses` module
+        "_generate_next_value_",
+        "_missing_",
+        "_numeric_repr_",
+    ],
+    (3, 13): ["_add_alias_", "_add_value_alias_"],
+}
 
 DUNDER_PROPERTIES = [
     "__class__",
diff --git a/pylint/extensions/dunder.py b/pylint/extensions/dunder.py
index 1683f81476..4d0fd65d65 100644
--- a/pylint/extensions/dunder.py
+++ b/pylint/extensions/dunder.py
@@ -41,11 +41,10 @@ class DunderChecker(BaseChecker):
     )
 
     def open(self) -> None:
-        self._dunder_methods = (
-            EXTRA_DUNDER_METHODS
-            + DUNDER_PROPERTIES
-            + self.linter.config.good_dunder_names
-        )
+        self._dunder_methods = DUNDER_PROPERTIES + self.linter.config.good_dunder_names
+        for since_vers, extra_dunder_methods in EXTRA_DUNDER_METHODS.items():
+            if since_vers <= self.linter.config.py_version:
+                self._dunder_methods.extend(extra_dunder_methods)
         for since_vers, dunder_methods in DUNDER_METHODS.items():
             if since_vers <= self.linter.config.py_version:
                 self._dunder_methods.extend(list(dunder_methods.keys()))