Attack RSA with very big module ($n$) and very small $e$ (7) As an exercise I'm given an RSA to attack. I have the module ($n$), the public exponent ($e$) and a single ciphertext ($c$).

For this particular case, $n$ is VERY big (5 thousand digits more or less), but the public exponent is small ($e=7$).

I know that, as $m \ll n$, this can cause no use of the module operation ($m^7\bmod n = m^7$). I tried reversing it doing $c^{1/7}=m^{7\cdot1/7}=m$ but this is not working.
It might be that $m^7 \bmod n \neq m^7$. What can I do in this case?

What am I missing/misunderstanding?

EDIT

I was given an hint: "Big $n$ is useless with small $e$". I assume it has more to do with the exponent rather then $n$.
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)