Inheritance. Here’s the solution code for this exercise (file adder.py), along with some interactive tests. The __add__ overload has to appear only once, in the superclass, as it invokes type-specific add methods in subclasses:

class Adder:
    def add(self, x, y):
        print('not implemented!')
    def __init__(self, start=[]):
        self.data = start
    def __add__(self, other):                    # Or in subclasses?
        return self.add(self.data, other)        # Or return type?

class ListAdder(Adder):
    def add(self, x, y):
        return x + y

class DictAdder(Adder):
    def add(self, x, y):
        new = {}
        for k in x.keys(): new[k] = x[k]
        for k in y.keys(): new[k] = y[k]
        return new

% python
>>> from adder import *
>>> x = Adder()
>>> x.add(1, 2)
not implemented!
>>> x = ListAdder()
>>> x.add([1], [2])
[1, 2]
>>> x = DictAdder()
>>> x.add({1:1}, {2:2})
{1: 1, 2: 2}

>>> x = Adder([1])
>>> x + [2]
not implemented!
>>>
>>> x = ListAdder([1])
>>> x + [2]
[1, 2]
>>> [2] + x
Traceback (innermost last):
  File "<stdin>", line 1, in ?
TypeError: __add__ nor __radd__ defined for these operands