7 deleted 199 characters in body
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05AB1E, 77 5 bytes

Ó0K3Å1QÓnO3Q

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Uses Luis Mendo'sDennis's algorithm.

Explanation:

Ó0K3Å1Q
Ó       Prime factor exponents
 0      0
  K     Filter out
   3    3
    Å1  List of x ones
      Q Equal? (True? 1 False? 0)

05AB1E, 7 bytes

Ó0K3Å1Q

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Uses Luis Mendo's algorithm.

Explanation:

Ó0K3Å1Q
Ó       Prime factor exponents
 0      0
  K     Filter out
   3    3
    Å1  List of x ones
      Q Equal? (True? 1 False? 0)

05AB1E, 7 5 bytes

ÓnO3Q

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Uses Dennis's algorithm.

6 added 59 characters in body
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05AB1E, 7 bytes

Ó0K3Å1Q

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Uses Luis Mendo's algorithm.

Explanation:

Ó0K7YвQÓ0K3Å1Q
Ó0KÓ     Non-zero prime Prime factor exponents
 0  3Å1  [1, 1, 1]0
  K     Filter out
   3    3
    Å1  List of x ones
      Q AreEqual? those(True? equal1 False? 0)

05AB1E, 7 bytes

Ó0K3Å1Q

Try it online!

Uses Luis Mendo's algorithm.

Explanation:

Ó0K7YвQ
Ó0K     Non-zero prime factor exponents
   3Å1  [1, 1, 1]
      Q Are those equal?

05AB1E, 7 bytes

Ó0K3Å1Q

Try it online!

Uses Luis Mendo's algorithm.

Explanation:

Ó0K3Å1Q
Ó       Prime factor exponents
 0      0
  K     Filter out
   3    3
    Å1  List of x ones
      Q Equal? (True? 1 False? 0)
5 edited body
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05AB1E, 7 bytes

Ó0K7YвQÓ0K3Å1Q

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Uses Luis Mendo's algorithm.

Explanation:

Ó0K7YвQ
Ó0K     Non-zero prime factor exponents
   7Yв3Å1  [1, 1, 1]
      Q Are those equal?

05AB1E, 7 bytes

Ó0K7YвQ

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Uses Luis Mendo's algorithm.

Explanation:

Ó0K7YвQ
Ó0K     Non-zero prime factor exponents
   7Yв  [1, 1, 1]
      Q Are those equal?

05AB1E, 7 bytes

Ó0K3Å1Q

Try it online!

Uses Luis Mendo's algorithm.

Explanation:

Ó0K7YвQ
Ó0K     Non-zero prime factor exponents
   3Å1  [1, 1, 1]
      Q Are those equal?
4 added 129 characters in body
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3 deleted 122 characters in body
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2 added 51 characters in body
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1
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