Attack RSA with very big module ($n$) and very small $e$ (7)
I found the problem: my implementation was incorrect. It was indeed a vulnerability where it happens that $m^e \mod n = m^e$. Below there is a Python implementation used to calculate it correctly (the value of $n$ and $c$ is redacted for privacy reasons).

from decimal import *

n = {redacted}
c = {redacted}
e = 7

# https://docs.python.org/3/library/decimal.html
c = Decimal(c)
e = Decimal(e)

getcontext().prec = 500 # Set a big enough precision
root = pow(c, 1/e) # Calculate c^(1/e) = m^(e * 1/e) = m
print(root)

# Decode with no padding
m = hex(int(root))[2:-1] # Number to hex
m = ''.join(chr(int(m[i:i+2], 16)) for i in range(0, len(m), 2)) # Hex to Ascii
print(m)